Electrical Capacitance Volume Tomography (ECVT) is a non-invasive imaging modality. Its applications span an array of industries. Most notably, ECVT is applicable to multiphase flow applications commonly employed in many industrial processes. ECVT is often the technology of choice due to its advantages of high imaging speed, scalability to different process vessels, flexibility, and safety. In ECVT, sensor plates are distributed around the circumference of the column, object or vessel under interrogation. The number of sensor plates may be increased to acquire more capacitance data. However, increasing the number of sensor plates reduces the area of each sensor plate accordingly. A limit exists on the minimum area of a sensor plate for a given column diameter, thus limiting the maximum number of plates that can be used in an ECVT sensor. This limit is dictated by the minimum signal-to-noise ratio requirement of the data acquisition system. Since ECVT technology is based on recording changes in capacitance measurements induced by changes in dielectric distribution (i.e., phase distribution), and the capacitance level of a particular sensor plate combination is directly proportional to the area of the plates, minimum signal levels are needed to provide sufficiently accurate measurements. These considerations dictate the required minimum sensor plate dimensions. This limitation on the minimum size of the sensor plates, while increasing the number of available sensor plates in an ECVT sensor, is one of the main hurdles in achieving a high resolution imaging system.
To overcome this challenge, the concept of Adaptive Electrical Capacitance Volume Tomography (AECVT) was recently developed, whereby the number of independent capacitance measurements is increased through the use of reconfigurable synthetic sensor plates composed of many smaller sensor plates (constitutive segments). These synthetic sensor plates maintain the minimum area for a given signal-to-noise ratio (SNR) and acquisition speed requirements while allowing for many different combinations of (synthetic) sensor plates in forming a sensor plate pair.
Electrical Capacitance Tomography (ECT) is the reconstruction of material concentrations of dielectric physical properties in the imaging domain by inversion of capacitance data from a capacitance sensor. Electrical Capacitance Volume Tomography or ECVT is the direct 3D reconstruction of volume concentrations or physical properties in the imaging domain utilizing 3D features in the ECVT sensor design. ECVT technology is described in U.S. Pat. No. 8,614,707 to Warsito et al. which is hereby incorporated by reference.
Adaptive Electrical Capacitance Volume Tomography (AECVT) provides higher resolution volume imaging of capacitance sensors based on different levels of activation levels on sensor plate segments. AECVT is described in U.S. Patent Application Publication US2013/0085365 A1 to Marashdeh et al. which is hereby incorporated by reference.
In ECT, ECVT, or AECVT, the capacitance measurement between sensor plates is also related to the effective dielectric content between that plate pair. The SART method can be extended to all measurements of ECT, ECVT, or AECVT sensors, thus providing a high resolution visual representation of each phase through image reconstruction.
Synthetic sensor plate formation is possible through advancements in the data acquisition technology that have enabled rapid separation in activation sources and the combination of the aggregated response from each segment of a given synthetic sensor plate. The total area of the segments combined can be made equivalent (or close) to that of a conventional ECVT sensor plate. Adaptive sensor plates can be used to increase the number of capacitance measurements and hence yield overall higher resolution imaging. Furthermore, AECVT plates can be used to adaptively modify the sensitivity of the output current to specific regions of interest in the imaging domain (where enhanced selective resolution may be desired) through the use of appropriate voltage patterns applied to the set of excitation sensor plates. To construct such voltage patterns, each segment is activated by different voltage levels thus forming a new sensitivity map. The use of different voltage patterns among individual segments that comprise a sensor plate also allows for a gradual taper of voltage levels between any two adjacent segments. This gradual tapering permits the use of higher peak voltages, and consequently increased SNR, without risk of dielectric breakdown (electrostatic discharges) occurring between the said segments.
AECVT is a novel technology that provides a significant increase in the number of possible independent capacitance measurements. However, increasing the number of independent measurements using AECVT technology only partially solves the resolution problems in capacitance-based tomography. Resolution is affected and determined by two other factors, in addition to AECVT sensor design: 1) suitable image reconstruction algorithms that can exploit the increase in information available from AECVT sensors, and 2) customized electronic design of high-speed measurement circuits utilized for AECVT sensors. The present invention specifically relates to the first factor above and comprises a new Spatial-Adaptive Reconstruction Technique (SART), which introduces a new image reconstruction technique that can take full advantage of the measurement capabilities provided by the AECVT sensor hardware design to achieve higher resolution imaging.
Extensive research has been done in the field of image reconstruction including non-iterative and iterative techniques. The most basic non-iterative image reconstruction technique is called Linear Back Projection (LBP) and is based on the assumption that a sensor can be modeled as a linear system where the overall capacitance change can be attributed to the linear superposition of local perturbations in the permittivity distribution within the imaging domain. Although LBP is able to provide very fast reconstruction, it gives very inaccurate reconstruction results when the spatial volume fraction, comprising the permittivity perturbation inside the imaging domain, is large and/or when the value of the relative permittivity of the said permittivity distribution is large. In addition to the LBP technique, Singular Value Decomposition (SVD) and Tikhonov methods have been used to regularize the final reconstructed image and to reduce the degree of ill-posedness of the problem. Moreover, to overcome the non-linearity of the problem, iterative reconstruction techniques also have been adopted. For example, Levenburq-Marquardt optimization techniques and Landweber techniques, based on the steepest gradient descent method, are used to minimize the squared error between measured and calculated capacitance data iteratively. Although iterative reconstruction techniques provide a better resolution compared to non-iterative reconstruction techniques, the former have convergence problems and require more computation time, which can be a drawback for some applications requiring real-time imaging. Historically, the resolution of either iterative or non-iterative techniques is limited by the soft-field nature of capacitance tomography, and by the ill-posedness and ill-conditioning of the inverse problem. The soft-field nature is related to the resolution being limited at the center of the imaging domain due to the Laplacian nature of the quasi-static field that interrogates the imaging domain (which has a self-averaging property of minimizing the average value taken over the surrounding points). This precludes the use of phase information and constructive/destructive interference to achieve focusing in certain regions of the domain (as can be done, for example, in microwave tomography). The present invention relates to new reconstruction algorithms poised to exploit the additional degree of freedom provided by the AECVT measurement acquisition hardware.
The new reconstruction methodology of the present invention, SART, is designed to utilize the flexibility of the AECVT technique in such a way that the imaging domain is divided into several regions where each region's permittivity distribution is reconstructed independently, based on “a priori” information about other region's calculated permittivity distributions. The algorithm iteratively reconstructs the spatial permittivity distribution of each separate region in the imaging domain until convergence is achieved. This process may also involve staggered iterative methods where each region is reconstructed iteratively and the independent regions are then combined into one image through another iterative optimization process. The basic principle behind this new reconstruction algorithm is that the fundamental resolution provided by the segment plates decreases monotonically from the periphery of the imaging domain close to the segment plates toward the center of the imaging domain far from the segment plates, due to the Laplace nature of interrogating the quasi-static electric field. Therefore, in electrical capacitance tomography applications, the field lines that penetrate into the middle of the imaging domain are always weaker and more spread-out compared to those closer to the sensor plates. The spatial sensitivity of any given capacitance sensor plates (to permittivity variations) is much greater at points in close vicinity to it when compared to points farther away from it. This causes the image resolution to progressively degrade at regions further away from the sensor plates.
By utilizing the SART method of the present invention and the reconfigurability of AECVT sensors, the sensitivity and hence resolution at the center of the imaging domain can be increased by taking advantage of information provided by an “a priori” reconstruction of the peripheral region. By utilizing near and adjacent plates, the overall resolution can be improved iteratively. As noted, iterative methods into themselves are not new in the field of electrical tomography systems. For example, the Distorted Born Iterative Method (DBIM) was used in impedance tomography reconstruction. However, those methods neither iterate over spatial regions adaptively nor exploit the flexibility of different excitation patterns enabled by AECVT.